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As a companion to the discussion on cavalry charging infantry (and to a conversation I was having at my club) what actually happened when the cavalry wings of the 2 sides met head on?  Did they literally charge full pelt into each other?  Did the horses physically collide?  Did they play chicken with each other?  Or was it more a case of slow manouvering, with pairs of horsemen (and the wings as a whole) trying to outfox each other?

Much of this would depend upon the cavalry, and their training and tactical repertoire.  Numidians would respond to a charge by about-turning and departing at speed, waiting until the chargers called a halt and then returning to pepper them with javelins.  Parthians and Iberians (as described by Tacitus) would loose arrows at each other, then charge in for a corps-a-corps struggle when they ran out of ammunition.  Crassus' Gallic cavalry at Carrhae charged straight into Parthian cataphracts and attempted to seize their spears and grapple them from their horses.

So it helps if we specify which cavalry types are engaging whom.  Classical javelin-armed cavalry would not behave in the same way as cataphract lance-armed cavalry.  Perhaps it would be worth looking up a few accounts of battles and asking what exactly goes on between the cavalry of two particular armies or nations.

Good question, though. :)

Was thinking of Cannae, Trebbia, Issus, Gaugamela : regular melee cavalry on the flanks charging frontally at each other then fighting until one side won.

This gives two Carthaginian vs Roman and two Macedonian (and Thessalian) vs miscellaneous Achameneid.  Extrapolating from what I know (or think I know) of the practices of the powers involved, plus (more importantly) the actual source descriptions, we get the following picture:

Cannae
On the Roman left, the Allied Italian cavalry, trained to melee face-to-face, are bewitched, bothered and bewildered by the Numidian cavalry swarming away every time the Italians look like charging and then swarming back as soon as the charge pulls up.  Appian suggests some concealed Numidians appeared on the Roman (i.e. Allied Italian) flank, which would have been a deterrent to folowing up the main body too determinedly.  Net result: stalemate, with very few people hurt.

The Roman right was very different; here Hannibal massed his Iberian and Gallic cavalry and sent them in against the Romans (and perhaps also the Extraordinarii, although the impression one gets is that these were on the left with Varro).  The Romans stood and fought, the result being practically an infantry melee on horseback, and as the Romans began losing they actually dismounted to try and give themselves extra steadiness.  Polybius III.115:

"But as soon as the Iberian and Celtic cavalry got at the Romans, the battle began in earnest, and in the true barbaric fashion: for there was none of the usual formal advance and retreat; but when they once got to close quarters, they grappled man to man, and, dismounting from their horses, fought on foot. But when the Carthaginians had got the upper hand in this encounter and killed most of their opponents on the ground,— because the Romans all maintained the fight with spirit and determination,—and began chasing the remainder along the river, slaying as they went and giving no quarter; then the legionaries took the place of the light-armed and closed with the enemy."

An interesting observation is that "there was none of the usual formal advance and retreat" (anastrophēs kai metabolēs), suggesting that anastrophe (wheeling around, of a horse) and metabole (exchanging, as by successive sub-units) were standard and expected tactics and procedures.  Also interesting is that both sides eschewed these standard tactics in favour of an all-out knock-down-drag-out fight.  The Carthaginians were trying to force a rapid conclusion with their superior numbers and the Romans had no ground to give without exposing the flanks of their army.

Having forced this conclusion, Hasdrubal took his cavalry en masse behind the rear of the Roman infantry and appeared on the flank of Varro's cavalry wing, which promptly took off at speed, harassed by the Numidians.  Hasdrubal then delivered his blow against the Roman infantry rear (which more properly pertains to another thread).

Trebia
The Trebia was more of a 'standard' cavalry action, although the Carthaginian preponderance in cavalry plus effective missile support (from slingers) rather skewed matters.  (On an elephant note, Hannibal committed his pachyderms against the Allied Italian infantry and not against the Roman and Italian cavalry.)  In this battle, the Roman (and Italian) cavalry did yield ground when overmatched, with unfortunate consequences for the poor Itlaian allies on the infantry wings.

"As soon, therefore, as their advanced guard had retired again within their lines, and the heavy-armed soldiers were engaged, the cavalry on the two wings of the Carthaginian army at once charged the enemy with all the effect of superiority in numbers, and in the condition both of men and horses secured by their freshness when they started. The Roman cavalry on the contrary retreated: and the flanks of the line being thus left unprotected, the Carthaginian spearmen (sc. peltasts) and the main body of the Numidians, passing their own advanced guard [i.e. working round the flanks], charged the Roman flanks: and, by the damage which they did them, prevented them from keeping up the fight with the troops on their front." - Polybius III.73

The Roman (including Italian) cavalry seem to have backpedalled in what we might characterise as a skirmishing retreat; most of them got away from the battlefield, indicating they had not been very closely engaged. 

These battles show that while there was an underlying doctrine of manoeuvre, it could be abandoned at the drop of a hat, and cavalry unaccustomed to Numidians could be upset by too much manoeuvre.

Now a look at Issus and Gaugamela.

Issus
At this battle, a few thousand Thessalian and Greek cavalry engaged a stated 30,000 Achaemenids attacking across a shallow river, and held them while the battle was won elsewhere.  Exactly how they did so is not specified, but the Persian cavalry would have been constrained by the narrow battlefield to deploy in very deep formation, so numbers in contact would have been about equal.  Tactics and techniques are not described; my own assumption is that the Thessalians, using the xyston, were well able to hold their own against the Achaemenid cavalry, who although better armoured were armed with the four-foot palta, a short javelin-spear.

Gaugamela
This has one of the most intricate and involved cavalry actions in our period.  The action on the Macedonian left is barely covered, and that only by Curtius, who tells us that Mazaeus 'pressed hard' against Parmenio and this pressure slackened when Darius fled, allowing Parmenio to mount a cautious counterattack which helped Mazaeus decide upon departure.

The Macedonian right fought a remarkable action against the Persian cavalry left, with odds similar to those at Issus.  Darius, seeing Alexander moving his army right to avoid Darius' trap, ordered in his chariots and cavalry, the cavalry on the Achaemenid left moving out en masse to sweep round the Macedonian right.  To perform this, they seem to have faced left and begun moving in what would have resembled a huge column.  Alexander sent out Menidas and his mercenary cavalry to intercept the Persians (actually mostly Scythians and Bactrians) by attacking the head of the column.  This worked; the Achaemenids redeployed to fight Menidas and were driving him back by weight of numbers and armour when Alexander added the Paeonians, here, as in all of his major battles, committed in an unambiguously shock role, together with the Greeks (xenous).  The Greeks, mercenaries and Paeonians gained the upper hand by anestrepsan, which suggests they fell back, drawing the Achaemenids on in some disorder, and then launched a coordinated charge which sent their opponents reeling.  (Curtius suggests Parmenio did something similar on his wing towards the close of the battle when Mazaeus' pressure slackened.)

Alexander improved upon this by promptly sending in the prodromoi/sarissophoroi (again, like the Paeonians, used in an unambiguous shock role against heavy opponents), catching the disordered Achaemenid cavalry left in flank and routing it off the field.  This left him clear to perform his own stroke through Darius' infantry left right into the centre where Darius himself was.  The results can be seen on the Alexander Mosaic.

Achaemenid cavalry seems to have conducted itself in a single large mass in which various contingents ebbed and flowed.  (There was one exception: 1,000 Indian and Persian cavalry were detached, or sent, to rescue the royal heir and incidentally help themselves to the Macedonian baggage; these performed their mission to the letter, forgoing opportunities to attack the phalanx in flank and rear.)  Alexander's cavalry fought by squadrons, able to act independently and also to launch massed coordinated charges.

General
On the minor detail front (speed of charge, what happens when men and mounts reach bump-together distance, etc.) we get little if any detail.  Curtius notes that Alexander's Companions were striking at their opponents' faces, which seems to have been Alex's preferred modus operandi, especially against armoured opponents.  Of interpenetration there seems to have been little or none; formations appear to have remained coherent and cohesive and, at least for the Macedonians, under control even after engaging.

In the examples Patrick gives I don't see any case of two cavalry bodies charging full-speed into each other, and IMHO I can't imagine horses being persuaded to charge into contact like this as horses (and riders) know they would come out of it the crippled losers. Cavalry seemed  to have halted when in sparring distance and then letting psychology and perhaps superior weaponry decide the issue.

It's possible though that in some cases the horses remain in constant movement by ranks charging and then countermarching, allowing the ranks behind them to charge in turn. Asklepiodotus describes squares in which the men in a file were three times further from each other than from men in adjacent files, whilst the formation preserved the shape of a square:

...the Greeks modified the squadron formation by making it an oblong in mass, while giving it to the eye the appearance of a square. For they drew up the riders with a front of sixteen and a depth of eight, but they doubled the interval between the riders because of the length of the horses. And some made the number of men in length three times that of the depth and then tripled the interval in depth, so that it again appeared to be a square... - Asklepiodotus 7: 4

Which gives this configuration:

(https://i.imgur.com/kLaucqa.png)

Notice that if the front rank countermarches to the rear the next rank has the distance to get up a good speed before contacting the enemy. It doesn't mean they charge into contact but it does create psychological intimidation and maybe the perceived threat of a disastrous contact. It also allows the rider with the longer lance to fatally wound his opponent as his weapon penetrates his opponent with the speed of his charge. An idea.

It is worth re-reading the Contemplating cavalry (http://soa.org.uk/sm/index.php?topic=3291.0) thread from earlier this year, where many of the same questions were explored.

I just read Justin's article in Slingshot 320 on the physics behind infantry stopiing (or at least slowing) a charging horse.  In calculating the number of ranks required to stop such a horse, he relies upon conservation of kinetic energy.  This is not the correct basis for such a calculation.

In accordance with Newton's First Law of Motion, momentum is conserved between colliding bodies, but not necessarily kinetic energy.  This is easily demonstrated in the classic experiment where one sticky body on a frictionless carriage is collided with a similar stationary sticky body.  Following collision, both bodies move at half the velocity of the single body prior to collision.  Momentum is conserved, but energy is not.

Applying this to the putative horse charging several infantrymen successively, what tends to happen is that the infantryman 'sticks' to the horse for a short period and is accelerated to around the same velocity as the horse, whose speed is consequently reduced in accordance with the Great Newton's observation above.

In the table below, I have taken Justin's figures for horse speed, mass of horse, etc.

Infantryman mass	70 kg
Horse initial speed	11.11 m/s
Horse mass	250 kg

I have also assumed that the horse and infantryman will be in contact for approximately 2 metres, during which time the latter will be accelerated to the same speed as the former.  From this can be calculated the acceleration and, hence, the force on the infantryman.

	Horse Speed	Horse Momentum	Combined Velocity	Infantry Momentum	Contact Time	Infantryman Acceleration	Infantryman Force
Rank	m/s	kg.m/s	m/s	kg.m/s	s	m/s2	N
1	11.1	2777.5	8.7	607.6	0.2	37.7	2636.8
2	8.7	2169.9	6.8	474.7	0.3	23.0	1609.4
3	6.8	1695.3	5.3	370.8	0.4	14.0	982.3
4	5.3	1324.4	4.1	289.7	0.5	8.6	599.5
5	4.1	1034.7	3.2	226.3	0.6	5.2	365.9
6	3.2	808.4	2.5	176.8	0.8	3.2	223.3
7	2.5	631.5	2.0	138.1	1.0	1.9	136.3
8	2.0	493.4	1.5	107.9	1.3	1.2	83.2

So what is the outcome?  Well, Justin calculated that the infantryman needed to experience a force of at least 307.8 N to be bowled over by the horse.  From the table it can be seen that the horse will knock over the first 5 infantry, but can probably be stopped by the sixth.  Any volunteers for the first 5 ranks?

That looks like a Guardroom piece waiting to happen.

250 kg sounds like a pretty small horse even in our period, though?

Quote from: Andreas Johansson on November 02, 2018, 09:56:01 AM250 kg sounds like a pretty small horse even in our period, though?

At https://digitalcollections.sit.edu/cgi/viewcontent.cgi?referer=https://www.google.co.uk/&httpsredir=1&article=2074&context=isp_collection 250 kg is cited as a typical weight for a Mongolian Darkhad horse; so lighter than you'd expect a cataphract to ride, perhaps, but not unreasonable.

But shouldn't we add the mass of the armed rider on top?

Quote from: Duncan Head on November 02, 2018, 10:01:38 AM
At https://digitalcollections.sit.edu/cgi/viewcontent.cgi?referer=https://www.google.co.uk/&httpsredir=1&article=2074&context=isp_collection 250 kg is cited as a typical weight for a Mongolian Darkhad horse; so lighter than you'd expect a cataphract to ride, perhaps, but not unreasonable.

I did say "pretty small", not "unreasonably small" :) I don't think steppe types on ponies are the most relevant for hitting solid infantry at speed. From a brief look online there seems to be considerable dispute about what medieval chargers weighed, but modern horses of similar height weigh 400+ kg, and warhorses presumably weren't more gracile than racehorses.

But re-reading Nick's post I see he says he took the number from Justin's piece (which I don't seem to've got around to reading), so if anyone it's him I should nitpick.

I just tried plufgging some numbers into my spreadsheet. 

Increasing the weight of horse by 10% increases the force on the infantryman by 22%.

Conversely, increasing the weight of the infantryman by 10% decreases the force by 12%.

All of which emphasises the importance of having a sturdy mount or big chaps in the front of your shieldwall, depending upon which side you find yourself on.   8)

Quote from: NickHarbud on November 02, 2018, 09:45:51 AM
I just read Justin's article in Slingshot 320 on the physics behind infantry stopiing (or at least slowing) a charging horse.  In calculating the number of ranks required to stop such a horse, he relies upon conservation of kinetic energy.  This is not the correct basis for such a calculation.

In accordance with Newton's First Law of Motion, momentum is conserved between colliding bodies, but not necessarily kinetic energy.  This is easily demonstrated in the classic experiment where one sticky body on a frictionless carriage is collided with a similar stationary sticky body.  Following collision, both bodies move at half the velocity of the single body prior to collision.  Momentum is conserved, but energy is not.

Applying this to the putative horse charging several infantrymen successively, what tends to happen is that the infantryman 'sticks' to the horse for a short period and is accelerated to around the same velocity as the horse, whose speed is consequently reduced in accordance with the Great Newton's observation above.

In the table below, I have taken Justin's figures for horse speed, mass of horse, etc.

Infantryman mass	70 kg
Horse initial speed	11.11 m/s
Horse mass	250 kg

I have also assumed that the horse and infantryman will be in contact for approximately 2 metres, during which time the latter will be accelerated to the same speed as the former.  From this can be calculated the acceleration and, hence, the force on the infantryman.

	Horse Speed	Horse Momentum	Combined Velocity	Infantry Momentum	Contact Time	Infantryman Acceleration	Infantryman Force
Rank	m/s	kg.m/s	m/s	kg.m/s	s	m/s2	N
1	11.1	2777.5	8.7	607.6	0.2	37.7	2636.8
2	8.7	2169.9	6.8	474.7	0.3	23.0	1609.4
3	6.8	1695.3	5.3	370.8	0.4	14.0	982.3
4	5.3	1324.4	4.1	289.7	0.5	8.6	599.5
5	4.1	1034.7	3.2	226.3	0.6	5.2	365.9
6	3.2	808.4	2.5	176.8	0.8	3.2	223.3
7	2.5	631.5	2.0	138.1	1.0	1.9	136.3
8	2.0	493.4	1.5	107.9	1.3	1.2	83.2

So what is the outcome?  Well, Justin calculated that the infantryman needed to experience a force of at least 307.8 N to be bowled over by the horse.  From the table it can be seen that the horse will knock over the first 5 infantry, but can probably be stopped by the sixth.  Any volunteers for the first 5 ranks?

Mmmmh... not quite. Have a look at the horse collision videos. The people hit by the horses are not borne along with them at their speed, certainly not for two metres, but are knocked flat immediately. They don't actually move from the spot where they were standing. So what you need to determine is the amount of force necessary to topple a standing man when hitting him in his middle, rather than the force necessary to get the entire human body moving at a speed just less than the horse's (which is slowed down by the impact).

But notice that even using this system, increase the weight of the horse slightly as suggested by Duncan and you can easily reach 7 ranks. I doubt that the rider contributes anything - if the horse slows down too much he is just pitched forward off the saddle.

@Andreas: I took 250KG as the lower end of the weight of horses in Antiquity, in order to produce results that were conservative and not exaggerations.

QuoteBut notice that even using this system, increase the weight of the horse slightly as suggested by Duncan and you can easily reach 7 ranks. I doubt that the rider contributes anything - if the horse slows down too much he is just pitched forward off the saddle.

It's an interesting mechanics question.  I think you have to consider the weight of the combined object but the object is in two parts, not strongly attached, so forces involved in deceleration could cause the object to separate into its constituent parts (i.e. the rider fall off).

Re Horse sizes, IIRC Duncan turned up some figures on Nisaen horses when we were discussing Persian logistics which put them in the 350-400kg range.  There is plenty of information about the height of ancient horses on line but not a lot on weight, probably because horses of the same height can vary quite a bit in weight depending on breed.   

What appears to be established is that a decent-sized horse can burst through an infantry line 8 ranks deep (a typical depth) unless the infantry do something about it. My guess is that they originally deployed in great depth before later switching to ranks bunched up together, othismos-like, which turned them into a stable mass a horse couldn't knock over.

Quote from: Erpingham on November 02, 2018, 11:41:02 AM
Re Horse sizes, IIRC Duncan turned up some figures on Nisaen horses when we were discussing Persian logistics which put them in the 350-400kg range.  There is plenty of information about the height of ancient horses on line but not a lot on weight, probably because horses of the same height can vary quite a bit in weight depending on breed.

Horse Mart has a table here (https://www.horsemart.co.uk/health/what-is-the-average-weight-of-a-horse-/659) showing approximate healthy weights for horses of different heights and breeds. As you'd guess, weight differs a lot by breed - a draught horse weighs about 50% more than a thoroughbred of the same height - but it seems reasonable to assume most (healthy) ancient horses were within the range of modern ones.

Quote from: Justin Swanton on November 02, 2018, 12:09:54 PM
What appears to be established is that a decent-sized horse can burst through an infantry line 8 ranks deep (a typical depth) unless the infantry do something about it. My guess is that they originally deployed in great depth before later switching to ranks bunched up together, othismos-like, which turned them into a stable mass a horse couldn't knock over.

...that and the pointy sticks probably put off the horses somewhat.

However we look at it, a determined horse and rider seem unlikely to be stopped by less than eight ranks of infantry, and then only if the infantry can provide some form of coherent grouping to reduce the impact and/or deterrence to avoid the impact taking place.

Arrian's lineup against the Alans is indicative: it has three ranks of kontoi, which provide deterrence both long and sharp (I am now entirely convinced that kontoi in this context cannot be understood as a term standing in for pila) and supporting missilemen behind.

All of this suggests that cavalry were, or could be, quite effective as an anti-infantry shock force unless the infantry were effectively trained, and preferably suitably equipped, to counter them.

Getting back to the purpose of the thread, namely the interaction of cavalry, we have a similar consideration except that the opposing troops are going to be of approximately equal mass and better able to manoeuvre to avoid a full-on collision.

So what are the aims and intentions of cavalry charging cavalry?

The obvious intent is to break the enemy formation or, on an individual level, to insert one's weapon into the enemy rider where it will do most good (or at least be most effective).  Usually this means a neck or body thrust or cut, but Alexander taught his troops to strike for the face, which if not an instant kill was a probable unhorsing.  One notes that in the Alexander Mosaic he appears to have ignored his own advice and run his opponent through the midriff.

At the Granicus, when Alexander himself was attacked, the one opponent (Rhoesaces) who landed a blow did so to his helmet, indicating the use of a slash rather than a cut, and Alexander responded with a thrust into the chest through the breastplate.  On the single occasion where he had room for a run-up, he used it to hit his opponent in the face with a xyston, knocking him to the ground.

Macedonian and Achaemenid cavalry, and probably others, appear to have placed a premium on formation-keeping while in melee.  Spithridates attempted to strike Alexander as the later was despatching Rhoesaces, but was anticipated and disarmed (literally, in Arrian's account) by Black Cleitus, who was presumably next-in-wedge behind and to the left of Alexander.

In order to keep formation in melee, contact would have to be disciplined rather than uninhibited.  This need not rule out contact at speed, rather it emphasises the need to keep station even at speed.  We do not however read of horses smacking together against each other and sitting down on their haunches from the impact, which suggests restraint in contact speed or care in aiming to contact the opposing line between two opposing horses, distributing any closure force into semi-cushioned angular impacts.  However I think the determining and limiting factor for contact speed was the need to be able to use weapons.  A full gallop is perhaps ruled out, although Roman cavalry apparently closed at speeds which made the points of their cuspides wobble, but speed of closure would seem to be considerably more than a controlled trot.

Firstly a comment on terminology.
This is not charging into contact...

Quote from: Patrick Waterson on October 12, 2018, 08:07:56 PM
Crassus' Gallic cavalry at Carrhae charged straight into Parthian cataphracts and attempted to seize their spears and grapple them from their horses.

You cannot "seize their spears" or "grapple" if you are actually charging. This is melee, not charging.
The example of Cannae, illustrates this.

If we don't have sources telling us that horse ploughed into each other, might we consider that it would be a stupendously silly thing to do. Quite apart from the high probability of crippling your horse, there would be a near 0 chance that the rider stays in the saddle if two charging horses actually collided. If you think that a horse can knock over 8 infantry men, consider that the potential acceleration for the riders of TWO HORSES colliding would be as much as twice as great as that suffered by the first infantrymen knocked over.

Quote from: Dangun on November 22, 2018, 03:32:53 AM
You cannot "seize their spears" or "grapple" if you are actually charging. This is melee, not charging.

But you can as soon as the charge results in contact.  The cavalry are not frozen in a state of perpetual charge;  upon contact the charge transitions to the melee.  I would also suggest that cavalry do not end up close enough to grapple without at least one side charging the other.

Quote... the potential acceleration for the riders of TWO HORSES colliding would be as much as twice as great as that suffered by the first infantrymen knocked over.

This is a common mistake (I blame the way physics and arithmetic are tauight in schools).  The acceleration, or more accurately momentum, of each rider is simply that imparted by his forward velocity, which does not double when he is suddenly halted.  If he is moving at, say, 15 mph prior to contact, he is still moving at 15 mph at the moment of contact, and 15 mph less the cushioning effect of his saddle, horse's neck etc. after contact.

Regarding colliding horses: I would suggest that the natural aim of a cavalryman is to try and place himself (and hence his mount) to deliver a stroke against an oncoming opponent, which is best achieved if he can get that opponent at a slight angle as opposed to straight ahead.  Hence when two formations of cavalry meet, each cavalryman will most probably be aiming to insert his horse between two horses in the enemy front rank, meanwhile attempting to insert his weapon into the enemy rider appearing ahead right or ahead left (the said rider will also be attempting to avoid the said weapon).  The result would be a coming together (if one may use the term) of both cavalry formations in a sort of saw-tooth pattern.

We might ask: what of the horses?  Newton's 'action and reaction are equal and opposite'* suggests that if two horses actually meet head-on (as opposed to the partial side-collisions the above would involve) then both will bouce back and be left sitting on their haunches.  If their riders have the type of saddle the Romans used, they will be left in position inelegantly leaning forwards; if not, they might well be departing for firmer ground at that point (and reaching it shortly afterwards).  But the partial impacts of offset horses are likely to be mutually absorbed with less fuss and consequences than we might expect.

*Seemingly inapplicable to missile weaponry, which appears to have its own rules.

Others have pointed out that when impact becomes inevitable, cavalry will tend to slow down somewhat in the final stages before impact.  Whether this was universally true I know not; indeed, I suspect that cavalry trained to accelerate as soon as they see opponents slow down would have a significant advantage in melee.  Be that as it may, there do seem to be numerous 'soft' factors which shade down the apparent simple physics of such collisions.

I'm no physicist but I'm sure this is wrong. I don't think acceleration is the relevant measure - the deceleration of horse A might depend only on the velocity of horse A at the point of impact (and granting for now that horses come to a dead stop on impact). But the energy or force applied depends on the combined velocity or momentum of horse A and horse B. Consider the difference in force applied and therefore damage caused between a horse heading north at 1 m/s stopping dead on encountering a stationary cannonball (damage to horse = negligible), and the same horse encountering a cannonball heading south at 300 m/s (damage to horse = severe). The velocity of both objects makes a big difference in an impact.

This needs more physics than I can conjour up but part of the issue is to decide what measures we think are significant.  The momentums of the two horses largely cancel out, because their velocities are in opposite directions (momentum has a vector, like velocity).  The energy of the collision, however, doesn't have a vector and the two kinetic energies are combined.  That energy will be converted into various things - heat, sound, deformation of/damage to horses and residual kinetic energy of the collided mass.

Quote from: RichT on November 22, 2018, 10:19:53 AM
I'm no physicist but I'm sure this is wrong. I don't think acceleration is the relevant measure - the deceleration of horse A might depend only on the velocity of horse A at the point of impact (and granting for now that horses come to a dead stop on impact). But the energy or force applied depends on the combined velocity or momentum of horse A and horse B.

I've lost track of quite where this discussion is going, but in terms of physics, acceleration is directly proportional to force. Newton's second law: force equals mass times acceleration

Kinetic energy is proportional to mass times speed squared. Because of the square, it does not relate simply to momentum (mass times velocity)

Force is what actually breaks bones and whatnot: having the same kinetic energy dissipated is going to have very different practical effects depending on how rapidly it is dissipated, which determines the peak forces you're subjected to.

(Consider slowing down from a run to stationary normally versus by running into a brick wall. You're shedding the same amount of kinetic energy in each case, but in the latter case you do so much more rapidly, so forces are much greater.)

I think we were getting hung up on the amount of forward kinetic energy a rider would have if his mount were to encounter another in full career.

Andreas has covered the essentials.  A couple of other points are worth mentioning.

The force of two horses colliding (if we can get them to collide head-on rather than offset) gives the horses a bump but not the riders.  The riders simply have to put up with a 15-to-0 deceleration which is usually handled by their saddle; failing that, the horse's neck. (If the horse puts its head down at the moment of stopping, the rider could well take a tumble unless held by a Roman-style saddle.)

Quote from: Erpingham on November 22, 2018, 11:10:21 AM
The energy of the collision, however, doesn't have a vector and the two kinetic energies are combined.

This is true of the horses - assuming a straight-line impact - but not of the riders.  The rider is not an integral part of the horse, and indeed articulates freely at the point of the saddle.  The riders only have to worry if both go sailing forward off their saddles into each other.

But would they go sailing forward off their saddles?  When TE Lawrence witnessed a charge of Arab camelry against Turkish cavalry, the greater mass of the camel bowled over the Turkish horse and rider together; the Turk did not immediately become separated from his mount.  I do not think we can simply apply the physics of a Newton's Cradle to cavalry impact.

Perhaps we should stop the mechanics bit, as it isn't advancing understanding?  I'm also losing track of what we set out to decide. 

I think the point at issue was what happened when man on mount collided with man on mount as the result of mutual high-speed closure.  (Actually it was whether the rider should be counted as going at 30 mph if two mounts met, each going at 15 mph.)  This has implications concerning whether a mutual full-on charge would result in shattered or merely rebuffed horses.

Classroom physics would seem to be a dead end; can anyone think of any contemporary accounts which might shed light on the matter?

Do you remember in Malory there were occasions when two knights' mounts collided full on?  I seem to recall that the result left both horses sitting back on their haunches as opposed to being blobs of jelly and bone chips.  A few saddles may have come apart in addition, and I cannot remember exactly where the riders ended up.  My assumption would be that Malory is reflecting and portraying the kind of thing his readers would expect from events in his own time; would this be a reasonable assumption?

Quote from: Patrick Waterson on November 23, 2018, 08:25:36 PM
can anyone think of any contemporary accounts which might shed light on the matter?

The absence of accounts is striking.

Quote from: Patrick Waterson on November 22, 2018, 09:07:01 AM
But you can as soon as the charge results in contact.  The cavalry are not frozen in a state of perpetual charge;  upon contact the charge transitions to the melee.  I would also suggest that cavalry do not end up close enough to grapple without at least one side charging the other.

So are you saying they charge, but stop short of the horse impacting another horse, and then start grappling?
What was the point of charging? Or do you mean you interpenetrate each other, for a complete loss of both side's cohesion. I really don't follow what is being suggested. This "charge" word is  ill defined.

Quote from: Dangun on November 24, 2018, 06:26:05 PM
So are you saying they charge, but stop short of the horse impacting another horse, and then start grappling?
What was the point of charging? Or do you mean you interpenetrate each other, for a complete loss of both side's cohesion. I really don't follow what is being suggested. This "charge" word is  ill defined.

What I am attempting to convey, however indifferently expressed, is that at Carrhae we have an example of two cavalry formations making intimate contact.

It is physically impossible to grapple an opposing rider without the horses having already inserted themselves into the opposing formation.  I would not imagine the Parthians obligingly held open gaps for the Gauls to walk their horses into before everyone began close quarters activity by mutual consent, which leaves us with one other option: they charged into contact.  Any grappling would take place after horses had impacted and/or avoided each other.

My understanding is that cavalrymen would aim to insert themselves into the gaps between opponents' horses.  If there are no gaps wide enough, then bumping equine shoulders with two opposing horses is preferable to bumping heads and/or chests with one.  It is also very difficult for cavalrymen to use their weapons against an opponent directly ahead - the horse's neck and head are in the way.  Hence one needs the target slightly offset to one side.

At Carrhae, the amount of interpenetration would be limited, perhaps only the first rank in each formation.  The formations themselves would be perhaps ten deep, so there would be no loss of cohesion from this cause.

Precisely defining 'charge' can be something of a challenge; the concept is essentially non-stop closure intended to result in melee and at greater speed than one's customary advance.  In short, closure with acceleration and impact.  The intention is usually that the impact be with one's weapon against an opponent, preferably in a suitable spot for disabling same.

Quote

QuoteQuote from: Patrick Waterson on November 23, 2018, 08:25:36 PM
    can anyone think of any contemporary accounts which might shed light on the matter?

The absence of accounts is striking.

Is it, though?  We lack accounts of most tactical procedures (hence the extensive discussions about same on these forums), so the lack of specific information on man-to-man (or horse-to-horse) encounters is not particularly noteworthy.

Quote from: Patrick Waterson on November 24, 2018, 07:30:56 PM


My understanding is that cavalrymen would aim to insert themselves into the gaps between opponents' horses.

I would suspect that there were always gaps wide enough, the unit couldn't maneuver if the horses were literally shoulder to shoulder. Also the riders legs would be trapped
There has to be some space and other horses would push into that space, probably at not much more than a walk by the time they got there (Because the actual pushing would slow them down a lot even if they did try it faster, the horses would act as a brake on each other)

QuoteThis has implications concerning whether a mutual full-on charge would result in shattered or merely rebuffed horses.

There are numerous images of horse v. horse collisions at speed on you tube.  They are not nice, as horses end up crippled or dead in several.  There is one good one in which two American quarter horses collide shoulder to shoulder at speed.  One horse and rider are sent sprawling.  The other horse stays on its feet but the rider goes over its neck.  Thankfully, both horses and riders survive this one.  So, from this small sample, we can probably say "shattering" isn't inevitable but it certainly happens.  This is also what you'd expect from any exposure to horse racing - not all falls and collisions result in death or serious injury but a proportion do.  The shoulder-to-shoulder collision is interesting in that you might expect a horse to avoid a head-to-head impact by angling its neck, with the impact being on the neck and shoulder, as in this case.

As to actual jousting practice, I've not read the many detailed accounts that exist to check them for collisions.  I would note though that the barrier or list between the two riders was introduced to reduce collisions and injuries to (very expensive) horses in the 15th century.

Quote from: Erpingham on November 25, 2018, 09:07:59 AM

QuoteThis has implications concerning whether a mutual full-on charge would result in shattered or merely rebuffed horses.

There are numerous images of horse v. horse collisions at speed on you tube.  They are not nice, as horses end up crippled or dead in several.  There is one good one in which two American quarter horses collide shoulder to shoulder at speed.  One horse and rider are sent sprawling.  The other horse stays on its feet but the rider goes over its neck.  Thankfully, both horses and riders survive this one.  So, from this small sample, we can probably say "shattering" isn't inevitable but it certainly happens.  This is also what you'd expect from any exposure to horse racing - not all falls and collisions result in death or serious injury but a proportion do.  The shoulder-to-shoulder collision is interesting in that you might expect a horse to avoid a head-to-head impact by angling its neck, with the impact being on the neck and shoulder, as in this case.

This is very useful; one obvious question would be the actual speed at which injuries start to result and particularly when they start to become the norm rather than the exception.  Cavalry charges in our period were not, as I understand it, conducted at racecourse speeds.

The effects of the collision on horse and rider are also worthy of note: they go down together or the horse stays up and the rider separates (he evidently was not using a Roman saddle!).

QuoteAs to actual jousting practice, I've not read the many detailed accounts that exist to check them for collisions.  I would note though that the barrier or list between the two riders was introduced to reduce collisions and injuries to (very expensive) horses in the 15th century.

A valid consideration, albeit one might also observe that it was not introduced until the 15th century, by which time the weights of both horses and armour had increased beyond what had been available throughout previous history.  Whether this lack of barrier introduction was because injuries were rarer or horses less precious is of course another question.

QuoteWhether this lack of barrier introduction was because injuries were rarer or horses less precious is of course another question.

It is usually assumed to be due to a change in jousting fashion.  One-on-one encounters on a narrow course were originally rarer than team melees in a wider arena.  As the one-to-one high speed encounters became more popular, serious collisions became more common so safety features were introduced.

I have had a look through various videos of equine head-on collisions.  One, in a 'sulky' (harness cart) race, had one horse plus 'sulky' going the wrong way around the track at speed while the rest of the field were going the correct way, at speed, and the resultant impact was lethal for both horses, although it was not clear whether death occured on impact or simply resulted from it (i.e. the animals being put down owing to broken bones or whatever).  Another, at a riding-in-mutually-interpenetrating-cricles rehearsal, conducted at the trot, saw both inexpert riders dumped on the ground but the horses were none the worse for wear.

Quote from: Erpingham on November 25, 2018, 11:49:27 AM

QuoteWhether this lack of barrier introduction was because injuries were rarer or horses less precious is of course another question.

It is usually assumed to be due to a change in jousting fashion.  One-on-one encounters on a narrow course were originally rarer than team melees in a wider arena.  As the one-to-one high speed encounters became more popular, serious collisions became more common so safety features were introduced.

That makes sense.

We may be closing in on a weight-and-speed combination above which direct contact at speed becomes potentially injurious to mount and conceivably man.  This speed would appear to be above a mutual trot and at or below a mutual gallop.  Historical charge speeds seem to have centred upon the canter, with exceptions (e.g. at Issus, Alexander went to the gallop to avoid Persian archery - the Impetus shooting evade in reverse!).  My instinct would be that cavalry quickly developed a 'feel' for the kind of speed which would provide impact without sustaining incapacitating injury, and that this speed would also be commensurate with control and cohesion.

There is a further consideration: in war, losses which would be unacceptable on the training field would be accepted if it was felt they provided a battle-winning edge.  Hence even if a number of injuries resulted from 'rough horseplay' these might be considered acceptable if they led to success.  This would allow us to raise our 'impact index' into the realm of risk of injury.

Quote from: NickHarbud on November 02, 2018, 09:45:51 AM

So what is the outcome?  Well, Justin calculated that the infantryman needed to experience a force of at least 307.8 N to be bowled over by the horse.  From the table it can be seen that the horse will knock over the first 5 infantry, but can probably be stopped by the sixth.  Any volunteers for the first 5 ranks?

I do not believe this is accurate. The horses do not collide as a solid mass.  If we assume that the infantry are in close order, essentially belly to back, by your calculations the horses would be stopped and the last 5 ranks knocked down like a Newton's cradle. But this does not happen, because the first horse hits the line of men and is stopped, then the second horse his the first horse and the line of men, third horse hits the first and second horse and the first horse and the line of men, etc.

We saw something similar when doing othismos experiments. Unless the hoplites are linked as one mass, the men ahead absorb much of the force from those behind. Arrian, by the way, tells us that horses cannot push in a linked manner as crowded men can.

Interesting....

The main purpose of my post was to point out that any calculations should be based upon conservation of momentum rather than conservation of kinetic energy, and that this would lead one to the conclusion that the effect of charging horses on a body of infantry would be somewhat less than calculated by Justin. 

Various videos that have been referenced seem to show that rather more momentum is transferred in the collision than I assumed and your practical experiments (with men) indicate that even this approach is somewhat optimistic from the viewpoint of the chargers.  In other words, instead of a charging horse ploughing through 7 ranks (as calculated by Justin) or 4 ranks (as calculated by me) it is probably a lower number, even assuming the horse is not put off by a solid line of infantry waving pointy sticks in its direction.

Incidentally, I accept no argument from ancient writers on the Laws of Motion.  Sir Isaac Newton tells us it is this way, and simply because one can demonstrate it in a classroom does not make it any less valid.   8)

Quote from: NickHarbud on December 04, 2018, 04:06:47 PM
Interesting....

The main purpose of my post was to point out that any calculations should be based upon conservation of momentum rather than conservation of kinetic energy, and that this would lead one to the conclusion that the effect of charging horses on a body of infantry would be somewhat less than calculated by Justin. 

Various videos that have been referenced seem to show that rather more momentum is transferred in the collision than I assumed and your practical experiments (with men) indicate that even this approach is somewhat optimistic from the viewpoint of the chargers.  In other words, instead of a charging horse ploughing through 7 ranks (as calculated by Justin) or 4 ranks (as calculated by me) it is probably a lower number, even assuming the horse is not put off by a solid line of infantry waving pointy sticks in its direction.

Incidentally, I accept no argument from ancient writers on the Laws of Motion.  Sir Isaac Newton tells us it is this way, and simply because one can demonstrate it in a classroom does not make it any less valid.   8)

Think of it as the difference between getting hit by a train car or getting hit by a few cars in line of the same mass.  Any space between them means that the opposing force, the men in our case, gets to act on them one at a time. (How much they decelerate each in turn before the next one hits is something that we would need to test, but a line like a hoplites would stop each horse dead almost instantly.  Here is a real example of something heavy, me, hitting a line of men.  I weigh about 300lbs, and I ran and jumped into a line of men three deep.  Smaller guys, lets say 160-170lbs and stationary.  I bounced off and they did not recoil.  Against one man, or even two they tend to recoil or fall. If a line of "me" hit in succession, they three man line would just absorb the strike.  Moreso because it is now a 4 man line with the first me having to be accelerated by the second me before effecting the line because I am not effectively part of the mass of the line:)

Just out of interest, here is a clip of a horse running into a car (https://uk.yahoo.com/news/runaway-horse-gallops-head-bmw-110000020.html).  'Runaway horse gallops head-on into a BMW'  (There may be a 20-30 second ad before the clip begins.)

Did anyone expect the actual result?

Quote from: Patrick Waterson on December 19, 2018, 09:42:46 AM
Just out of interest, here is a clip of a horse running into a car (https://uk.yahoo.com/news/runaway-horse-gallops-head-bmw-110000020.html).  'Runaway horse gallops head-on into a BMW'  (There may be a 20-30 second ad before the clip begins.)

Did anyone expect the actual result?

That's one lucky horse.  Usually what happens is far worse.  I wouldn't recommend this for animal lovers but the are many examples here (https://www.google.com/search?q=horse+collision&client=firefox-b-ab&source=lnms&tbm=isch&sa=X&ved=0ahUKEwibzPCJ2KvfAhXOZlAKHeieAUgQ_AUIDigB&biw=1440&bih=786).

Yes.  I think 'head on' in the headline was a little misleading: from what I saw the horse impacted at an angle and rolled onto the bonnet.  It does at least show how a difference in the angle of collision (i.e. not being directly head-on) can make a big difference to the result.